Maple bugs: the next freeze frame calculated by GEMM
Vladimir Bondarenko
Detailed analysis reveals that quality of Maple 9 and the
reasons behind the current Maple status as well as the
instructive lessons one can learn from this topic grow
out of the Maple user community scope: that is why this
message is sent to this newsgroup.
At http://www.cybertester.com/ we promised you "Search over
5000 distinct Maple bugs not later than on Apr 10, 2004"
We keep our word: today, on our local Apr 10, 11 p.m., yet
another step has been done; you can explore our next sketch.
Even more, we are pleased to announce that we already have
essentially more data on Maple bug manifestations than we
have presented; we already have different, more convenient
and powerful structures; the deployment of the Maple Bugs
Encyclopaedia has its internal logics and stages; in the
near future, before your eyes our GEMM machine will weave,
in several steps, a self-consistent unique tapestry helping
you to deal with Maple more efficiently.
Welcome to a thrilling world of thousands Maple bugs!
Onward,
Vladimir Bondarenko
GEMM architect
Co-founder, CEO, Mathematical Director
Cyber Tester, LLC
http://www.cybertester.com/
http://maple.bug-list.org/
http://www.CAS-testing.org/
............................................................
steve_H
Do you include among your bugs the maple 9 Java GUI related
problems?
If so, this byitself will require a whole web site to contain,
and so it might not be fair to maple core bugs and will tilt the scale
in a way which might not reflect the true state of affairs.
I no longer even start maple 9 java GUI. It is so bad, if you just
blow air on it, it will crash or hangs. But I have to say this is no
fault of maplesoft, which I am sure have the best
engineers, it is simply that Java does not belong on the desktop. If
you must blame someone, blame Sun for this.
This is the reason why one does not see commerical shrink-wrapped
GUI based applications written in Java. Java belongs on the server-side.
v...@cybertester.com (Vladimir Bondarenko) wrote in message news:<72ufxv0ke36q@legacy>...
Vladimir Bondarenko
On 11 Apr 2004 03:41:04 -0700, steve_H wrote:
SH> Do you include among your bugs the maple 9 Java GUI related
SH> problems?
According to Maplesoft's web servers,
"Maplesoft is a world leader in mathematical and analytical software."
http://www.maplesoft.com/products/maple/explore.shtml
"Maple 9 is the premium software system for any activity that involves
mathematics."
http://www.maplesoft.com/support/
"Maplesoft is committed to providing the highest level of support
for the products it sells."
Leader? Premium? Highest? OK, let's consider concrete examples.
Maple 9.03> is(sin(z)^2 + cos(z)^2 = 1);
false
Maple 9.03> is(0..1 = 0..2);
Error, (in property/ConvertRelation) invalid relation\
arguments
Maple 9.03> solve(1+(1+z^2)^(5/2)=0, z);
Error, (in evala/Indep) argument should be an algebraic\
function field
Maple 9.03> int(1/z, z=I..2*I); (!) # Table integral for a frosh
Float(infinity) # = ln(2)
Maple 9.03> int(exp(z), z= I..a); # Table integral for a frosh
Error, (in Limit) Limit uses a 3rd argument, dir, which\
is missing
exp(a)-exp(I)
Maple 9.03> int(arccoth(z), z= 0..1); # Table integral for a frosh
ln(2)+1/2*I*Pi # = ln(2)-1/2*I*Pi
Maple 9.03> restart; int(z^(2/3), z=1..10); # 2 (!) invalid answers
# when asked repeatedly
-3*3^(1/2)*GAMMA(2/3)*(1/15*Pi*3^(1/2)/GAMMA(2/3)-2/3*25\
^(1/2)*Pi/GAMMA(2/3))/Pi
-1/3*3^(1/2)*GAMMA(2/3)*(-6*75^(1/2)*3^(1/2)*Pi/GAMMA(2/\
3)+3/5*Pi*3^(1/2)/GAMMA(2/3))/Pi
Maple 9.03> int(sqrt(exp(z)+sinh(z)), z= 0..infinity);
KERNEL FAILURE
Maple 9.03> int(sqrt((z+1)^2)/z, z= 0..1);
1 # = infinity
Maple 9.03> int(ln(abs(z^2-1))/(1+z)^2, z= 0..infinity);
KERNEL FAILURE # 1
Maple 9.03> int(sqrt((z+1)^2), z = 0..1);
1/2 # = 3/2
Maple 9.03> evalf(Int(1/z^2, z= I..infinity)); # Table integral
Error, (in evalf/int) non-numeric integration limit\
encountered
-1.*I
Maple 9.03> evalf(Int(I*z, z= 1..0));
Error, (in evalf/int) contradictory assumptions
Maple 9.03> evalf(subs(t= 1/3, int(I*z/(t+z), z= 0..t-1)));
Error, (in evalf/int) contradictory assumptions
Maple 9.03> evalf(Sum(1, n= 1..infinity));
0. # = Float(infinity)
Maple 9.03> evalf(Int(HermiteH(1,1/z), z=0..1));
KERNEL FAILURE
Maple 9.03> evalf(Int(sin(Pi*z)/floor(z), z= 1..infinity));
Float(infinity) # = -.4412712002 = -2*ln(2)/Pi
Maple 9.03> evalf(JacobiZeta(1, 1));
40000 sec - nothing
First and foremost, we are interested in the same things as the
most (or all) of the users: detecting Maple's bad math results.
SH> If so, this by itself will require a whole web site to contain,
SH> and so it might not be fair to maple core bugs
There are hundreds distinct bugs in GUI. There are many THOUSANDS
distinct bugs in math. Relax, the core bugs first.
SH> and will tilt the scale in a way which might not reflect the
SH> true state of affairs.
Don't worry, be happy ;)
SH> I no longer even start maple 9 java GUI. It is so bad, if you
SH> just blow air on it, it will crash or hangs.
There are at least many hundreds distinct ways to crash Maple 9.
Maple 9.03> int(abs(1-sqrt(z)),z=0..I*Pi);
KERNEL FAILURE
Maple 9.03> evalf(Int(hypergeom([],[1-z],1/3), z= 1..2));
KERNEL FAILURE
Maple 9.03> evalf(Int(BesselJ(0, z)^2, z= 0..infinity));
KERNEL FAILURE
Maple 9.03> evalf(Int(1/(sqrt(1+z)+sqrt(1-z)), z=
-infinity..infinity));
KERNEL FAILURE
Maple 9.03> evalf(Int(cot(z)/frac(z), z= 0..Pi/2*I));
KERNEL FAILURE
Maple 9.03> evalf(Int(hypergeom([], [z], 1/2), z= 0..infinity,
_CCquad));
KERNEL FAILURE
SH> But I have to say this is no fault of maplesoft
Gee, you do have a a keen sense of humor! "no fault of maplesoft"
Who then made the decision of using Java? You? Me? Maplesoft leaders?
SH> If you must blame someone, blame Sun for this.
If a drunk driver hit a pedestrian, will his relative sue Ford?
Or the driver?
Best wishes,
Vladimir Bondarenko
.....................................................................
steve_H
> Leader? Premium? Highest? OK, let's consider concrete examples.
>
I tried your examples on mma, opps, I mean MATHEATICA, 5.0
to compare. Here are the results.
> Maple 9.03> is(sin(z)^2 + cos(z)^2 = 1);
>
> false
>
mma gives same answer:
In[1]:= Sin[z]^2+Cos[z]^2 ===1
Out[1]= False
TrueQ[Sin[z]^2 + Cos[z]^2 == 1]
False
does the above identity depend on the domain Z is defined over?
I mean, may be in general it is not true? (where is my calculus book
when I need it). I mean both mma and maple agree on this, so
it must be true :)
> Maple 9.03> is(0..1 = 0..2);
>
> Error, (in property/ConvertRelation) invalid relation\
> arguments
>
In[3]:= Range[0,1]===Range[0,2]
Out[3]= False
> Maple 9.03> solve(1+(1+z^2)^(5/2)=0, z);
>
> Error, (in evala/Indep) argument should be an algebraic\
> function field
>
In[6]:= Solve[1+(1+z^2)^(5/2)==0,z]
Out[6]= 5 Sqrt[5] I 5 + Sqrt[5]
z -> -Sqrt[-(-) + ------- - - Sqrt[-----------]]
4 4 2 2
5 Sqrt[5] I 5 + Sqrt[5]
z -> Sqrt[-(-) + ------- - - Sqrt[-----------]]
4 4 2 2
5 Sqrt[5] I 5 + Sqrt[5]
z -> -Sqrt[-(-) + ------- + - Sqrt[-----------]]
4 4 2 2
5 Sqrt[5] I 5 + Sqrt[5]
z -> Sqrt[-(-) + ------- + - Sqrt[-----------]]
4 4 2 2
> Maple 9.03> int(1/z, z=I..2*I); (!) # Table integral for a frosh
>
> Float(infinity) # = ln(2)
In[8]:= Integrate[1/z,{z,I,2*I}]
Out[8]= Log[2]
>
> Maple 9.03> int(exp(z), z= I..a); # Table integral for a frosh
>
> Error, (in Limit) Limit uses a 3rd argument, dir, which\
> is missing
>
> exp(a)-exp(I)
>
In[9]:= Integrate[Exp[z],{z,I,a}]
I a
Out[9]= -E + E
> Maple 9.03> int(arccoth(z), z= 0..1); # Table integral for a frosh
>
> ln(2)+1/2*I*Pi # = ln(2)-1/2*I*Pi
In[12]:= Integrate[ArcCoth[z],{z,0,1}]
-I
Out[12]= -- Pi + Log[2]
2
>
> Maple 9.03> restart; int(z^(2/3), z=1..10); # 2 (!) invalid answers
> # when asked repeatedly
>
> -3*3^(1/2)*GAMMA(2/3)*(1/15*Pi*3^(1/2)/GAMMA(2/3)-2/3*25\
> ^(1/2)*Pi/GAMMA(2/3))/Pi
>
> -1/3*3^(1/2)*GAMMA(2/3)*(-6*75^(1/2)*3^(1/2)*Pi/GAMMA(2/\
> 3)+3/5*Pi*3^(1/2)/GAMMA(2/3))/Pi
>
I tried the above on my maple, and it does give it in terms of
GAMMA function (which is nothing but the factorial when the argument
is integer btw). doing evalf on the output from the intergal gives:
16.72050808
this is mma output:
In[13]:= Integrate[z^(2/3),{z,1,10}]
3 2/3
Out[13]= -(-) + 6 10
5
In[14]:= N[%]
Out[14]= 27.2495
So clearly we have different numerical values. so one is wrong. wonder
who? :)
> Maple 9.03> int(sqrt(exp(z)+sinh(z)), z= 0..infinity);
>
> KERNEL FAILURE
>
This one mma could not do, either (but no Kernel failure message).
(may be just the maple message is the wrong message?)
In[15]:= Integrate[Sqrt[Exp[z]+Sinh[z]],{z,0,Infinity}]
Integrate::idiv:
z
Integral of Sqrt[E + Sinh[z]] does not converge on
{0, Infinity}.
z
Out[15]= Integrate[Sqrt[E + Sinh[z]], {z, 0, Infinity}]
> Maple 9.03> int(sqrt((z+1)^2)/z, z= 0..1);
>
> 1 # = infinity
>
This one mma did not do btw.
In[18]:= Integrate[Sqrt[ (z+1)^2 ]/z,{z,0,1}]
Integrate::gener: Unable to check convergence.
Integrate::idiv:
2
Sqrt[(1 + z) ]
Integral of -------------- does not converge on {0, 1}.
z
2
Sqrt[(1 + z) ]
Out[18]= Integrate[--------------, {z, 0, 1}]
z
> Maple 9.03> int(ln(abs(z^2-1))/(1+z)^2, z= 0..infinity);
>
> KERNEL FAILURE # 1
>
In[19]:= Integrate[Log[Abs[z^2-1]]/(1+z)^2,{z,0,Infinity}]
Out[19]= 1
> Maple 9.03> int(sqrt((z+1)^2), z = 0..1);
>
> 1/2 # = 3/2
>
In[20]:= Integrate[ Sqrt[ (z+1)^2 ],{z,0,1}]
3
Out[20]= -
2
> Maple 9.03> evalf(Int(1/z^2, z= I..infinity)); # Table integral
>
> Error, (in evalf/int) non-numeric integration limit\
> encountered
>
> -1.*I
>
In[25]:= Integrate[1/z^2,{z,I,Infinity}]
Out[25]= -I
> Maple 9.03> evalf(Int(I*z, z= 1..0));
>
> Error, (in evalf/int) contradictory assumptions
>
In[26]:= Integrate[I*z,{z,1,0}]
-I
Out[26]= --
2
> Maple 9.03> evalf(subs(t= 1/3, int(I*z/(t+z), z= 0..t-1)));
>
> Error, (in evalf/int) contradictory assumptions
>
here also mma complains. different message wording?
In[28]:= Integrate[I*z/(t+z),{z,0,t-1}];
In[29]:= % /. t-> 1/3
Integrate::gener: Unable to check convergence.
Integrate::idiv:
z
Integral of -------- does not converge on {0, 1}.
-1 + 2 z
-2 I -2 z
Out[29]= ---- Integrate[-----------, {z, 0, 1},
3 1 2 z
3 (- - ---)
3 3
> Assumptions -> True]
> Maple 9.03> evalf(Sum(1, n= 1..infinity));
>
> 0. # = Float(infinity)
>
Big difference between 0 and infinity!
In[30]:= Sum[1,{n,1,Infinity}]//N
Out[30]= Infinity
> Maple 9.03> evalf(Int(HermiteH(1,1/z), z=0..1));
> KERNEL FAILURE
>
>
here also mma did not do it. (ofcourse it blows up at z=0)
may be message difference only?
In[32]:= Integrate[HermiteH[1,1/z],{z,0,1}]
1
Integrate::idiv: Integral of - does not converge on {0, 1}.
z
2
Out[32]= Integrate[-, {z, 0, 1}]
z
> Maple 9.03> evalf(Int(sin(Pi*z)/floor(z), z= 1..infinity));
>
> Float(infinity) # = -.4412712002 = -2*ln(2)/Pi
humm.. mma gives -7.3
In[35]:= NIntegrate[Sin[Pi*z]/Floor[z],{z,1,Infinity}]
NIntegrate::slwcon:
Numerical integration converging too slowly; suspect one
of the following: singularity, value of the integration
being 0, oscillatory integrand, or insufficient
WorkingPrecision. If your integrand is oscillatory try
using the option Method->Oscillatory in NIntegrate.
NIntegrate::ncvb:
NIntegrate failed to converge to prescribed accuracy after
11
7 recursive bisections in z near z = 7.72261 10 .
Out[35]= -7.31356
In[36]:=
>
> Maple 9.03> evalf(JacobiZeta(1, 1));
> 40000 sec - nothing
>
In[37]:= JacobiZeta[1,1]
Out[37]= JacobiZeta[1, 1]
In[38]:= N[%]
Out[38]= 0.841471
answer right away.
> Maple 9.03> int(abs(1-sqrt(z)),z=0..I*Pi);
>
> KERNEL FAILURE
>
this mma could do it also symbolically, but it did it numerically.
(I tried this on maple, but it seems to make it froze)
In[40]:= Integrate[Abs[1-Sqrt[z]],{z,0,I*Pi}]
Out[40]= Integrate[Abs[1 - Sqrt[z]], {z, 0, I Pi}]
In[41]:= N[%]
N::meprec: Internal precision limit $MaxExtraPrecision = 50.
reached while evaluating
Integrate[Abs[1 - Sqrt[z]], {z, <<2>>}].
Out[41]= 0. + 2.92559 I
> Maple 9.03> evalf(Int(hypergeom([],[1-z],1/3), z= 1..2));
>
> KERNEL FAILURE
>
mma has so many hypergeometric functions, do not know which is
the generalized one, so I skip on this...
> Maple 9.03> evalf(Int(BesselJ(0, z)^2, z= 0..infinity));
>
> KERNEL FAILURE
>
In[43]:= Integrate[BesselJ[0,z]^2,{z,0,Infinity}]
EulerGamma + Log[8]
Out[43]= -------------------
Pi
In[44]:=
In[44]:= N[%]
Out[44]= 0.84564
> Maple 9.03> evalf(Int(1/(sqrt(1+z)+sqrt(1-z)), z=
> -infinity..infinity));
>
> KERNEL FAILURE
>
In[45]:= Integrate[1/(Sqrt[1+z]+Sqrt[1-z]),{z,-Infinity,Infinity}]
Integrate::idiv:
1
Integral of -------------------------
Sqrt[1 - z] + Sqrt[1 + z]
does not converge on {-Infinity, Infinity}.
1
Out[45]= Integrate[-------------------------,
Sqrt[1 - z] + Sqrt[1 + z]
> {z, -Infinity, Infinity}]
In[46]:= N[%]
NIntegrate::slwcon:
Numerical integration converging too slowly; suspect one
of the following: singularity, value of the integration
being 0, oscillatory integrand, or insufficient
WorkingPrecision. If your integrand is oscillatory try
using the option Method->Oscillatory in NIntegrate.
NIntegrate::ncvb:
NIntegrate failed to converge to prescribed accuracy after
56
7 recursive bisections in z near z = -2.28833 10 .
1750 1750
Out[46]= 8.1699036391 10 - 8.1699036391 10 I
In[47]:=
> Maple 9.03> evalf(Int(cot(z)/frac(z), z= 0..Pi/2*I));
>
> KERNEL FAILURE
>
In[51]:= NIntegrate[Cot[z]/FractionalPart[z],{z,0,Pi/2*I}]
NIntegrate::slwcon:
Numerical integration converging too slowly; suspect one of the following:
singularity, value of the integration being 0, oscillatory integrand, or
insufficient WorkingPrecision. If your integrand is oscillatory try using the
option Method->Oscillatory in NIntegrate.
NIntegrate::ncvb:
NIntegrate failed to converge to prescribed accuracy after 7
-57
recursive bisections in z near z = 0. + 6.86437 10 I.
3497
Out[51]= 0. - 7.89825617234 10 I
> Maple 9.03> evalf(Int(hypergeom([], [z], 1/2), z= 0..infinity,
> _CCquad));
>
> KERNEL FAILURE
>
mma has so many hypergeometric functions, do not know which is
the generalized one, so I skip on this...
>
> Best wishes,
>
> Vladimir Bondarenko
>
> http://www.cybertester.com/
> http://maple.bug-list.org/
> http://www.CAS-testing.org/
>
thanks for your work, may you find more bugs :)
Richard Fateman
and get their responses, if any. Some of them are perhaps
deliberate designs, in which case your note could be much
more cogent. Some of them may be user (i.e. your) error,
in which case maybe you might decide not to post them here.
Usually, long messages are a bad idea, especially ones that
are a random assortment of statements like "can you believe this??"
interspersed with computer output of error messages.
If you want to write an article comparing various systems
(including perhaps mupad, reduce, axiom, ...) on what they do
in various cases, you will have to make sure that you have used
each of them correctly. You will need to understand what
the commands actually are supposed to do, as opposed to what
you might guess they do. The paper by M. Wester could be
a guide for you.
Regards
RJF
Christopher Creutzig
>> Maple 9.03> is(sin(z)^2 + cos(z)^2 = 1);
>>
>> false
>>
>
> mma gives same answer:
>
> In[1]:= Sin[z]^2+Cos[z]^2 ===1
>
> Out[1]= False
>
> TrueQ[Sin[z]^2 + Cos[z]^2 == 1]
>
> False
>
> does the above identity depend on the domain Z is defined over?
> I mean, may be in general it is not true? (where is my calculus book
> when I need it). I mean both mma and maple agree on this, so
> it must be true :)
No, it doesn't, at least as long as you assume them to be complex.
(Has anyone checked the equality for matrices?) Then again, just
about any simplification does assume that. Try
FullSimplify[Sin[z]^2+Cos[z]^2]
Oh, and while we are comparing: MuPAD works pretty well on these
examples, too -- but then again, they have been carefully selected to
show Maple bugs, not to be representative of typical mathematical
usage. :-)
MuPAD 3.0 >> is(sin(z)^2 + cos(z)^2 = 1) // Ouch -- but not wrong
UNKNOWN
MuPAD 3.0 >> testeq(sin(z)^2 + cos(z)^2, 1)
TRUE
MuPAD 3.0 >> is(0..1 = 0..2)
FALSE
MuPAD 3.0 >> solve(1+(1+z^2)^(5/2)=0, z)
{ / / 1/2 2 1/2 1/2 1/2 \1/2
{ | | ((5 - 3) - 2 5 + 10) 5 |
{ | | ------------------------------ + ---- - 3/2 |
{ \ \ 2 2 /
{
{
...
MuPAD 3.0 >> int(1/z, z=I..2*I) // could be a bit better, but correct
ln(2 I) - 1/2 I PI
MuPAD 3.0 >> Simplify(%)
ln(2)
MuPAD 3.0 >> int(exp(z), z= I..a)
exp(a) - exp(I)
MuPAD 3.0 >> int(arccoth(z), z= 0..1)
ln(2) - 1/2 I PI
MuPAD 3.0 >> int(z^(2/3), z=1..10)
2/3
6 10 - 3/5
> This one mma could not do, either (but no Kernel failure message).
Same for MuPAD.
> (may be just the maple message is the wrong message?)
I think Vladimir actually meant a system crash.
>> Maple 9.03> int(sqrt((z+1)^2)/z, z= 0..1);
>>
>> 1 # = infinity
>>
>
> This one mma did not do btw.
Same for MuPAD. (And there are actually users complaining "But
Maple gives a result" and don't care that the result is completely
wrong. Now what's a programmer to do with that?)
MuPAD 3.0 >> int(ln(abs(z^2-1))/(1+z)^2, z= 0..infinity)
1
MuPAD 3.0 >> int(sqrt((z+1)^2), z = 0..1)
3/2
>> Maple 9.03> evalf(Int(1/z^2, z= I..infinity)); # Table integral
Here the Maple call explicitly ignores symbolic integration.
> In[25]:= Integrate[1/z^2,{z,I,Infinity}]
>
> Out[25]= -I
This is symbolic.
MuPAD 3.0 >> int(1/z^2, z= I..infinity)
-I
MuPAD 3.0 >> numeric::int(1/z^2, z= I..infinity)
2.710505431e-20 - 1.0 I
MuPAD 3.0 >> numeric::int(I*z, z= 1..0)
-0.5 I
MuPAD 3.0 >> float(subs(int(I*z/(t+z), z= 0..t-1), t=1/3))
-0.6666666667 I
>> Maple 9.03> evalf(Sum(1, n= 1..infinity));
Again, this is a numerical evaluation, bypassing (presumably) all
symbolic manipulation.
MuPAD 3.0 >> sum(1, n= 1..infinity)
infinity
MuPAD 3.0 >> numeric::sum(1, n= 1..infinity)
numeric::sum(1.0, n = 1..infinity)
>> Maple 9.03> evalf(Int(HermiteH(1,1/z), z=0..1));
MuPAD doesn't know HermiteH. :(
>> Maple 9.03> evalf(Int(sin(Pi*z)/floor(z), z= 1..infinity));
>>
>> Float(infinity) # = -.4412712002 = -2*ln(2)/Pi
>
> humm.. mma gives -7.3
MuPAD thinks Vladimir is (roughly) right, but it's a tough problem:
MuPAD 3.0 >> numeric::int(sin(PI*z)/floor(z), z= 1..infinity)
/ sin(PI z) \
numeric::int| ---------, z = 1..infinity |
\ floor(z) /
MuPAD 3.0 >> numeric::quadrature(sin(PI*z)/floor(z), z= 1..infinity)
Warning: Precision goal not achieved after 10000 function calls!
Increase MaxCalls and try again for a more accurate result. [numeric::quad\
rature]
-0.4240830523
MuPAD 3.0 >> numeric::quadrature(sin(PI*z)/floor(z), z= 1..infinity, MaxCalls = 200000)
Warning: Precision goal not achieved after 200000 function calls!
Increase MaxCalls and try again for a more accurate result. [numeric::quad\
rature]
-0.4416564549
>> Maple 9.03> evalf(JacobiZeta(1, 1));
MuPAD doesn't have that, either.
The next one, MuPAD solves obviously incorrectly:
MuPAD 3.0 >> int(abs(1-sqrt(z)),z=0..I*PI)
/ 3/2 \
1/2 | 2 (I PI) |
- sign(1 - (I PI) ) | ----------- - I PI |
\ 3 /
MuPAD 3.0 >> float(%)
- 0.01360707877 - 2.675263294 I
MuPAD 3.0 >> numeric::int(abs(1-sqrt(z)),z=0..I*PI)
2.925593099 I
> In[40]:= Integrate[Abs[1-Sqrt[z]],{z,0,I*Pi}]
>
> Out[40]= Integrate[Abs[1 - Sqrt[z]], {z, 0, I Pi}]
>
> In[41]:= N[%]
>
> N::meprec: Internal precision limit $MaxExtraPrecision = 50.
> reached while evaluating
> Integrate[Abs[1 - Sqrt[z]], {z, <<2>>}].
>
> Out[41]= 0. + 2.92559 I
But Mathematica is no better. (Integrate[Abs[...], {...}] must yield
a non-negative real result, no?)
MuPAD 3.0 >> numeric::int(hypergeom([],[1-z],1/3), z= 1..2) // no result
numeric::int(hypergeom([], [1 - z], 1/3), z = 1..2)
MuPAD 3.0 >> numeric::int(besselJ(0, z)^2, z= 0..infinity)
2
numeric::int(besselJ(0, z) , z = 0..infinity)
MuPAD 3.0 >> numeric::quadrature(besselJ(0, z)^2, z= 0..infinity)
Warning: Precision goal not achieved after 10000 function calls!
Increase MaxCalls and try again for a more accurate result. [numeric::quad\
rature]
3.23604102
MuPAD 3.0 >> numeric::int(1/(sqrt(1+z)+sqrt(1-z)), z=-infinity..infinity)
/ 1 \
numeric::int| -----------------------, z = -infinity..infinity |
| 1/2 1/2 |
\ (z + 1) + (1 - z) /
MuPAD 3.0 >> numeric::quadrature(1/(sqrt(1+z)+sqrt(1-z)), z=-infinity..inf$
Warning: Precision goal not achieved after 10000 function calls!
Increase MaxCalls and try again for a more accurate result. [numeric::quad\
rature]
6.417522826e16 - 6.417522826e16 I
MuPAD 3.0 >> numeric::int(cot(z)/frac(z), z= 0..PI/2*I)
/ cot(z) \
numeric::int| -------, z = 0..1/2 I PI |
\ frac(z) /
MuPAD 3.0 >> numeric::quadrature(cot(z)/frac(z), z= 0..PI/2*I)
Warning: Precision goal not achieved after 10000 function calls!
Increase MaxCalls and try again for a more accurate result. [numeric::quad\
rature]
-19.62648953 I
MuPAD 3.0 >> numeric::int(hypergeom([], [z], 1/2), z=0..infinity)
numeric::int(hypergeom([], [z], 1/2), z = 0..infinity)
MuPAD 3.0 >> numeric::quadrature(hypergeom([], [z], 1/2), z=0..infinity)
Error: Overflow/underflow in arithmetical operation;
during evaluation of 'hypergeom::float'
:-(
--
+--+
+--+|
|+-|+ Christopher Creutzig (c...@mupad.de)
+--+ Tel.: 05251-60-5525
Christopher Creutzig
> But Mathematica is no better. (Integrate[Abs[...], {...}] must yield
> a non-negative real result, no?)
I realized yestaerday while walking home that this was nonsense.
Thanks to those who sent me a friendly note on that topic.
Bhuvanesh
> v...@cybertester.com (Vladimir Bondarenko) wrote:
>
> > Leader? Premium? Highest? OK, let's consider concrete examples.
> >
>
> I tried your examples on mma, opps, I mean MATHEATICA, 5.0
> to compare. Here are the results.
You do realize you're pretty much advertising Mathematica with your
comparison, right? :-)
Cheers,
Bhuvanesh,
Wolfram Research.
--
Disclaimer: Any opinions expressed herein are my own and not
necessarily those of Wolfram Research.
Vladimir Bondarenko
>nma...@hotmail.com (steve_H) wrote:
>> v...@cybertester.com (Vladimir Bondarenko) wrote:
>>
>> > Leader? Premium? Highest? OK, let's consider concrete examples.
>> >
>>
BB> You do realize you're pretty much advertising Mathematica
BB> with your comparison, right? :-)
Sorry for breaking in upon your dialogue, but do you really
want a different direction? ;) If yes then please tell me,
and 'on my word you will be amazed with the outcome of your
request 8)
By the way, for a long time I keep eye on your postings here
and there as well as your homepage and testing remarks, and I
like them, really. You have light nice style like Andy Shiekh.
Especially, I am eager to enjoy at last your wonderful aunt's
homepage... but visiting regularly this link I understand that
great achievements should not come quickly 8-)
BTW do you still use Derive/TI calculator occasionally?
Just curious.
Cheers,
Vladimir
--
Vladimir Bondarenko
Cyber Tester, LLC
...........................................................
Bhuvanesh
> Sorry for breaking in upon your dialogue, but do you really
> want a different direction? ;) If yes then please tell me,
> and 'on my word you will be amazed with the outcome of your
> request 8)
Do you mean your bug list for Mathematica (especially Integrate)?
> By the way, for a long time I keep eye on your postings here
> and there as well as your homepage and testing remarks, and I
> like them, really. You have light nice style like Andy Shiekh.
Perhaps that's not a coincidence. Andy and I are very good friends.
> Especially, I am eager to enjoy at last your wonderful aunt's
> homepage... but visiting regularly this link I understand that
> great achievements should not come quickly 8-)
LOL! She was never very much into computers or the Internet, so I gave
up updating her webpage after a while...
> BTW do you still use Derive/TI calculator occasionally?
> Just curious.
Oh, yes. Actually, they sometimes help me at work when testing
Mathematica. The big advantages of the TI-68k are portability and that
they use operating systems that are smaller and more stable than
computer OS's.
Cheers,
Bhuvanesh.